Question

Evaluate: $\frac{cos^2 32\textdegree + cos^2 58\textdegree }{cos^2 59\textdegree + cos^2 31\textdegree} + sin 90\textdegree - tan 45\textdegree + cos 0\textdegree$

Answer 1

we have to evaluate : ( cos²32° + cos²58° )/(cos²59° + cos²31°) + sin90° - tan45° + cos0°

we know, cos(90° - A) = sinA
cos32° = cos(90° - 58°) = sin58°
so, cos²32° + cos²58° = sin²58° + cos²58° = 1.....(1)

similarly, cos59° = cos(90° - 31°) = sin31°
so, cos²59° + cos²31° = sin²31° + cos²31° = 1......(2)

now, ( cos²32° + cos²58° )/(cos²59° + cos²31°) + sin90° - tan45° + cos0°

we know, sin90° = 1, tan45° = 1 and cos0° = 1

from equations (1), (2)

= 1/1 + 1 - 1 + 1

= 1 - 1 + 1

= 1 [ans ]

Answer 2

Answer:

2

Step-by-step explanation:

The very first term i.e. the fraction should be reduced to a simpler form.

We have to use the formula: cos(90-θ) = sinθ.

Similiarly, cos²32° = cos²(90-58)° = sin²58°

and cos²59° = cos²(90-31)° = sin²31°.

Also we know that sin²θ + cos²θ = 1.

Therefore,

$\frac{cos²32° + cos²58°}{cos²59° + cos²31°}$ + sin90° - tan45° + cos0°

or, $\frac{sin²58° + cos²58°}{sin²31° + cos²31°}$ + sin90° - tan45° + cos0°

or, $\frac{1}{1}$ + 1 - 1 + 1   [Because, sin90° = tan45° = cos0° = 1]

or, 1 + 1 - 1 + 1

or, 2 [Ans]